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A certain company that sells only cars and trucks reported t

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A certain company that sells only cars and trucks reported t  [#permalink]

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New post 11 Mar 2014, 23:04
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3

Problem Solving
Question: 155
Category: Algebra; Arithmetic First-degree equations; Percents
Page: 82
Difficulty: 600


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A certain company that sells only cars and trucks reported that  [#permalink]

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New post 12 Mar 2014, 22:07
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1
getzgetzu wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3


This is a weighted average question. Average of -11% and +7% is +1%.
Using w1/w2 = (A2 - Aavg)/(Aavg - A1),
we get w1/w2 = (7 - 1)/(1- (-11)) = 6/12
Revenue from Car:Revenue from Trucks = 1:2

For explanation of the formula and other details, go to:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/

For another discussion on the same question, check: a-certain-company-that-sells-only-cars-and-trucks-reported-73058.html#p541483
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 11 Mar 2014, 23:04
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SOLUTION

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3

Let the revenue from cars in 1996 be \(c\) and revenue from trucks in 1996 be \(t\).

Total revenue in 1997 would be \(0.89c+1.07t\).
Also as total revenue in 1997 were up 1 percent from 1996, then total revenue in 1997 would be \(1.01(c+t)\).

Equate above two: \(0.89c+1.07t=1.01(c+t)\) --> \(\frac{c}{t}=\frac{1}{2}\).

Answer: A.
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 12 Mar 2014, 18:43
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Answer = (A) 1:2

Please refer chart below:
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 12 Mar 2014, 19:15
1
The company sells only cars and trucks.
Let c = revenue from car sales in 1996
Let t = revenue from truck sales in 1996
Equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997,
c(0.89) + t(1.07) = (c+t) (1.01)
Dividing throughout by t,
(c/t) (0.89) + 1.07 = (c/t + 1) (1.01)
=> (c/t) (0.12) = 0.06
=> (c/t) = 1/2

Option (A).
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 15 Mar 2014, 19:49
1
This is how my brain processed this one,

Step 1 --> Set up the equations.

In 1996: R = C+T
In 1997: 1.01R = .89C+1.07T

Remember we are looking for C/T.

Step 2 --> Substitute

1.01(C+T) = .89C+1.07T or,
1.01C + 1.01T = .89C+1.07T

Step 3 --> Solve

.12C = .06T
.12C/T = .06
C/T = .06/.12
C/T = 1/2 or 1:2

Answer is (A) :-D
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 20 May 2014, 12:26
3
1
Car-------------------------------Truck
(-11%)-----------------------------(+7%)
-------------------------(+1%)-------- (Wtd Avg)
--------(12%)------------/----(6%)--
Thus ratio of Car Sales/Truck Sales = 6/12= 1/2

FWIW, this is one of the fastest and easiest way to solve such problems
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 15 Dec 2016, 21:55
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3
Attachments

Screen Shot 2016-12-16 at 1.50.41 PM.png
Screen Shot 2016-12-16 at 1.50.41 PM.png [ 340.19 KiB | Viewed 3760 times ]

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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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New post 29 Jul 2017, 20:05
Here is a simpler solution
X=Cars
Y= Trucks.

Obviously intuitively for sales to grow Y would need to be bigger than X as X was negative and Sales overall were positive.
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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Re: A certain company that sells only cars and trucks reported t &nbs [#permalink] 12 Aug 2018, 19:02
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